How do I find out the force on a mast?

As a purely theoretical exorcise I was looking at what it would take to put a powered motor on a mast to rotate the mast and boom rather than a sheet on a moving boom. Now, I know any powered system has all kinds of issues with reliability vs. a standard rig. But I still wanted to figure out what size powered motor would be needed to handle the forces that a strong force wind would apply to the motor at the base of the mast. I've found motors for rotating large antenna arrays that have a ft. lb. rating for wind resistance. So now I'm trying to find out what kind of pressures would be applied to this motor if it was attached to a mast, fixed boom and sail.

So I was looking for a formula that would tell me the ft. lbs of rotation pressure for a given mast height and boom length and a known wind in knots.

Now, I know there are all kinds of issues involved, but before I even look at those I just wanted to see if any of these motors are even in the ball park.

Of course, the other question is... has anyone ever see a powered rotating mast on a sailing yacht?

 

Anything with proper gearing.. It actually boils down how fast (or slow) you are willing to turn the mast and sail..

 

Are you thinking of a sheetless rig where the boom is rigidly attached to the mast? The motor would then rotate the mast to affect sail trim. If that is the case then torque requirements might vary all over the lot. You will have introduced variables beyond sail area, aspect ratio, and wind velocity.

You may be thinking of some variation of the so called "swing rig". If the rig has a jib as most of them do, then there is a whole other set of variables with which you must contend. To clarify "swing rig" it goes like this....... The boom is rigidly attached to the mast but is free to pivot in the vertical plane. The boom extends forward of the mast for some distance. The jib luff wire is attached to the forward end of the boom and the jib is sheeted to the boom extension near the mast. That is a crafty way to avoid vangs because the jib luff wire tends to depress the clew end of the main. The whole thing revolves about the mast center line and the jib relieves some of the strain on the mainsheet by partially counterbalancing the main. Not only that but the jib and the main are always in the same spacial relationship with one another. There are other factors that would seem to constitute some sort of advantage, like when on a dead run you need not pole the jib, etc.

This a rig that a lot of RC modelers have tinkered with. It works. In no case have I seen of one of these rigs that is sheetless but I confess to having tossed the idea around in my sick mind. Some of the RC modelers claim that downwind behavior is erratic but I have not experienced that problem with models. There are some other references to this kind of rig on the forum.

 

Sounds like you are tending towards a wing mast. Messabouts ideas are balancing aero forces about the mast, which makes a lot of sense as there could be some extremely high rotational forces to be contended with. In wing theory, center of lift is approximately 25% cord. Devising a system where your center of lift is located at the mast centerline would reduce control forces tremendously.

Otherwise, rotational force is roughly moment arm times force. A crude estimate will place center of effort 1/3 of the distance aft of the luff (triangular rig). With a 15' boom, C/E would give you a 5 ft moment arm. If your sail is producing 100 lbs. of lift then you've got 500 ft.lbs. torque on the mast. If your sail is producing 1000 lbs. (?) of lift, then you've got 5000 ft.lbs. of torque on the mast. These should "ballpark" you if you are brainstorming something. Basic physics. Actual dynamic forces could cause things to vary.

Good Luck.

 

LP, thank you so much for your reply. It's very close to giving me the ball park number I'm looking for, but maybe you could help me a little more if I gave you some dimensions. What if the mast sail area was 20 meters (or 65') in height and the boom 6 meters (or 20') in length, and the wind was coming at 50 knots? How would this calculate (in the roughest of measurements is fine) into ft.lbs of torque on the mast?

I'm looking at a chart of different rotators that have these Breaking Torques:
in/lbs 1) 29,163 2) 71,607 3) 102,072 4) 159,358 5) 428,773
Each of these is a different rotator, but they are getting larger and heavier.

And I'm trying to see if any of them can handle the torque of a sail that large in a stiff wind.
Thanks!

 

I would think a bigger problem would be to design a mast that would withstand the torque.

 

You can use the heeling moment of the boat to estimate the force on the sail. As indicated earlier, heeling moment at 30 degrees is pretty normal.

You know that, whatever the forces are on the sail, they are applying a moment that big to the boat. Solve for the force at the geometric center of the sail.

Now use the horizontal arm, as indicated earlier, to work out the moment applied to the mast.

The heeling moment of the boat is what matters most here. If your boat basically falls over in a breeze, the maximum force on the sail is going to be quite low. If your boat is immensely stable, then the wind can pick up quite a lot, and apply a great deal of force to the sail before the boat heels enough to spill much breeze and take the load off.

 

From Skene's book on design, wind pressure is equal to .004*V^2(mph)*area(ft^2). Somebody jump in and tell me if I am completely misinterpreting theory here. Basic triangle: .5BH=.5*65*20=650ft^2.

50kts*1.15=57.5mph.

57.5^2=3306.

.004*3306=13.2lbs/ft^2

13.2*650ft^2=8595lbs.force.

8595*1/3=2865ft.lbs. torque

2865*12=34,380 in.lbs. torque

This could be a gross misinterpretation of design theory. Skene doesn't state whether this wind pressure is driving force(lift) created by the sails of if it is pressure created by any physical object as it stands in a wind stream. Personally, there are so many unknowns here, I'm hessitant to even present these numbers.

There are certainly other factor to contend with also. A big issue is how are you going to maintain sail shape. Close to the wind, your main sheet supplies a great amount of vanging force to flatten your sail.

Anyways, good luck and I hope you build a model first.

 

To simplify we can say the center of the force is at the center of the sail.
Using the moment arm formula: t= r * F
In this case r=B/2 happens to be the middle of the boom.
32.5 ft * 8595lbs.force = 279337.5 ft lbs torque

 

use one pound wind pressure per square foot of sail area will give you a reasonable number. That would be high for most recreational sails, low for a wing sail.

Generally they consider force on the sail limited by the maximum righting moment the keel can generate, so that would limit maximum wind pressure on the sail. So you would need the hull design, keel wt, etc to determine actual loads.

 

Thank you all for your information, I'm trying to get some rough numbers now.

 

LP,
I know these are grossly ball park numbers, but they do give me some hope since the rotator motor I was considering was 73,000 in/lb. rotating torque and 102,000 in/lb. braking torque. If the numbers had been so far off that it was ridiculous I would have dropped the whole idea. This is now enough for me to at least consider spending some money on an naval architect, test model, etc. There are still a lot of hurdles to overcome before I would ever consider actually trying to build a yacht with this system, right now this is just a fun exorcise in strange ideas.

You mentioned a problem with keeping sail shape correct. How is this different than an Aerorig with the exception that I would be power rotating the mast? (And possibly not having the jib fixed on its own forward facing boom). How did that design keep the sail shape?
http://www.yachtforums.com/forums/technical-discussion/6528-rotating-aerorig-2.html

Someone was also talking about the mast itself being strong enough, and someone mentioned spilling due to heeling and keel weight calculations. My thoughts on all this are to make this a catamaran, use an unstayed carbon fiber mast that will flex at high wind strengths to spill off excess force in a strong gust.

Any issues and problems noted from this idea? I'm pretty sure there are quite a few. I'm not currently planning to actually build this (beyond a model) so it's fine to tell me this is a hair brained idea, but if so, please tell me why. But what I would really like to hear is how to solve any perceived issues with this concept.

 

I don't understand why you wouldn't rotate the whole assembly from the end of the boom instead of from the base of the mast.

You've already got the boom there, it's kind of inherent in the design. Why not clap a tackle on the end of it, and use the lever you've already built? I'd have to think it through, but this may actually take load OFF of the boom, so you get to built a lighter structure as well.

 

This would miss the whole point of this exorcise, which is to make a powered mast that requires no sheet. Obviously, traditional sheet and tackle works, but that's not what I'm trying to explore. I've already built several boats with traditional rigs.

Don't worry, my insanity isn't limited to this crazy idea. If I work out how to make this work, next I'm going to look into power raising and lowering the sail. If that is feasible, then next I'm going to hook the whole shabang up to a computer an have the boat sail itself. I'll tie in the GPS, wind speed and direction, and write a program that will have the boat sail itself to where you tell it to go. Now, do I think I'll actually build this as a real yacht? Well, I could win the lottery, but short of that, probably not. Would I build a model of it? Well, maybe, just to have some fun. I might even build a small boat, large enough to be fun, maybe a two person size and then I can watch it sail around Mission Bay on it's own. I can program the thing myself, but I need help figuring out the mechanics and limitations, which is why I'm here.

But telling me that this isn't the way that it's been done before is contrary to the point of this strange idea, I'm TRYING to do it wrong (or different might be a better word). I like to explore new ways of doing things, and this is my current wild idea to spend some money and time messing around with. In the end, I just want to know if it CAN be done.

 

it seems to me that unless your mast is round with a sleeve type sail (not a good shape for sail efficiency) if you allow the mast to flex to spill excess wind, it would not want to rotate very well, or it could bind up.

Cantilevered masts have be attempted, they tend to add a lot of weight. The advantage is you loose all the drag from the rigging, and one of the reasons external rigging has disappeared off of aircraft wings about 70 years ago. However on low speed sailboats the drag is relatively small and the weight and cost savings are worth a bit of extra rigging drag. I suspect that on faster multi-hulls there would be significant gains by eliminating or at least reducing the drag of the external rigging.

In your case you are attempting a cantilevered mast with a rotating base, and a motor to rotate it too. There would have to be pretty significant performance increase to justify that much weight and complication. It will be an interesting experiment.

Good luck